Square Root Of 250047 In Simplest Radical Form
Simplify the square root of 250047 to its lowest radical form.ANSWER: 189√7
189√7 is in the lowest radical form.
Simplified Radical Form of √250047
One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y
Explanation:
When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.
Step 1: List Factors
To simplify √250047, we need to divide into factors.
√250047 = √3 x √3 x √3 x √3 x √3 x √3 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 250047
9 is a perfect square and divides 250047
49 is a perfect square and divides 250047
81 is a perfect square and divides 250047
441 is a perfect square and divides 250047
729 is a perfect square and divides 250047
3969 is a perfect square and divides 250047
35721 is a perfect square and divides 250047
Step 3: Divide To Perfect Square
Divide 250047 by the largest perfect square you found in the previous step:
Step 4: Calculate The Square Root
Calculate the square root of the largest perfect square:
Final Step :
Put Steps 3 and 4 together to get the square root of 250047 in its simplest form: 189√7
How do you simplify √250047
The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.
Find the lowest prime number that can divide 250047. Divide 250047 repeatedly using the long division method till you reach 1.
A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.
Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.
So, the answer is 189√7.
Simplified Decimal Form of √250047
The square root of 250047 is approximately 500.047 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √53 | Square root of 53 is the simplest radical form. | √53 |
| √7 | Square root of 7 is the simplest radical form. | √7 |
| √56 | 2√14 | √2 x √2 x √2 x √7 |
| √214 | Square root of 214 is the simplest radical form. | √2 x √107 |
| √669 | Square root of 669 is the simplest radical form. | √3 x √223 |
| √869 | Square root of 869 is the simplest radical form. | √11 x √79 |
| √2498 | Square root of 2498 is the simplest radical form. | √2 x √1249 |
| √6182 | Square root of 6182 is the simplest radical form. | √2 x √11 x √281 |
| √9572 | 2√2393 | √2 x √2 x √2393 |